Hm... I tried to make a Golly ruletable for the X-rule based on Figure 12 in the paper, but it didn't quite work out.

I took 'descending order of neighborhood values' to mean counting down, in binary, from 111111111 to 000000000 - where the first digit represents the current cell and the remaining eight represent its Moore neighborhood - matching each row of the image to 64 numbers. (e.g. the first row, 0001001001100000000000010000010000101000011110100000010000010011, went to the neighbor counts 111111111 through 111000000.)

# The first digit represents the current cell, the next eight its Moore neighborhood, and the final digit determines that configuration's 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(note that this is unoptimized in a number of ways; for instance, 'stay-the-same' - 0->0 or 1->1 - transitions don't need to be specified, and there are ways of using variables to shrink the table's size)

M. I. Wright wrote:Hm... I tried to make a Golly ruletable for the X-rule based on Figure 12 in the paper, but it didn't quite work out.

I took 'descending order of neighborhood values' to mean counting down, in binary, from 111111111 to 000000000 - where the first digit represents the current cell and the remaining eight represent its Moore neighborhood - matching each row of the image to 64 numbers. (e.g. the first row, 0001001001100000000000010000010000101000011110100000010000010011, went to the neighbor counts 111111111 through 111000000.)...Any idea what I'm doing wrong?

It's a good theory. The paper really doesn't explain this well at all -- unless I'm missing seeing a little diagram somewhere that shows which neighbor (or central cell) corresponds to the first bit, which neighbor to the second bit, etc., in 111111111 through 000000000.

There are 512 little squares in that diagram. You must have that part of the mapping right.

But there's no guarantee that they want the leftmost bit to mean the center cell. Could it be that the 1st, leftmost bit is the upper-left cell, the 5th bit is the center cell, and the 9th, rightmost bit is the lower-right cell? That's the mapping I'd bet on, if you haven't tried it.

There are a few other mappings of bits to neighbors that might make sense, like leftmost bit=center cell, then assign neighbors clockwise from the top center, or from the top left, or just left-to-right then top-to-bottom.

There's an interesting diagonal bilateral symmetry in each of the 8x8 boxes in Figure 12. I assume that corresponds to the rotations and reflections that they talk about, that reduce the space from 2^512 to 2^102.

It should be possible to use those diagonal lines of symmetry to deduce the center/neighbor mapping -- but maybe a little more trial and error will be easier!

dvgrn wrote:But there's no guarantee that they want the leftmost bit to mean the center cell. Could it be that the 1st, leftmost bit is the upper-left cell, the 5th bit is the center cell, and the 9th, rightmost bit is the lower-right cell? That's the mapping I'd bet on, if you haven't tried it.

There are a few other mappings of bits to neighbors that might make sense, like leftmost bit=center cell, then assign neighbors clockwise from the top center, or from the top left, or just left-to-right then top-to-bottom.

Whoops, I've gotten used to Golly's rule format! I'd be willing to be that it's your first suggestion, actually.

There's an interesting diagonal bilateral symmetry in each of the 8x8 boxes in Figure 12. I assume that corresponds to the rotations and reflections that they talk about, that reduce the space from 2^512 to 2^102.

It should be possible to use those diagonal lines of symmetry to deduce the center/neighbor mapping -- but maybe a little more trial and error will be easier!

Oh shoot, I completely missed that (both the symmetry in the rule-table and the mention of rotations/reflections - I skimmed over 2.1 at first and didn't see other mentions of symmetry). It might be easier to figure out the rule format (and where the center cell lies in the transition) knowing that the precursor has rotate4reflect symmetry, although I've got nothing for now - I'll wait until jmgomez (hopefully) replies before attempting anything new with the ruletable.

Edit - Alternatively: Is anyone familiar with Mathematica's rule format? The note at the bottom says that X-rule was tested in the language, so it might make sense for the image to correspond with that.

dvgrn wrote:But there's no guarantee that they want the leftmost bit to mean the center cell. Could it be that the 1st, leftmost bit is the upper-left cell, the 5th bit is the center cell, and the 9th, rightmost bit is the lower-right cell? That's the mapping I'd bet on, if you haven't tried it.

Yup, I think that's got it. Just had to shuffle the bits in the columns of the first rule table, in a very headache-inducing way:

# The first digit represents the current cell, the next eight its Moore neighborhood, and the final digit determines that configuration's output# C,N,NE,E,SE,S,SW,W,NW,C'1,1,1,1,1,1,1,1,1,01,1,1,1,0,1,1,1,1,01,1,1,1,1,0,1,1,1,01,1,1,1,0,0,1,1,1,11,1,1,1,1,1,0,1,1,01,1,1,1,0,1,0,1,1,01,1,1,1,1,0,0,1,1,11,1,1,1,0,0,0,1,1,01,1,1,0,1,1,1,1,1,01,1,1,0,0,1,1,1,1,11,1,1,0,1,0,1,1,1,11,1,1,0,0,0,1,1,1,01,1,1,0,1,1,0,1,1,01,1,1,0,0,1,0,1,1,01,1,1,0,1,0,0,1,1,01,1,1,0,0,0,0,1,1,00,1,1,1,1,1,1,1,1,00,1,1,1,0,1,1,1,1,00,1,1,1,1,0,1,1,1,00,1,1,1,0,0,1,1,1,00,1,1,1,1,1,0,1,1,00,1,1,1,0,1,0,1,1,00,1,1,1,1,0,0,1,1,00,1,1,1,0,0,0,1,1,10,1,1,0,1,1,1,1,1,00,1,1,0,0,1,1,1,1,00,1,1,0,1,0,1,1,1,00,1,1,0,0,0,1,1,1,00,1,1,0,1,1,0,1,1,00,1,1,0,0,1,0,1,1,10,1,1,0,1,0,0,1,1,00,1,1,0,0,0,0,1,1,01,1,1,1,1,1,1,0,1,01,1,1,1,0,1,1,0,1,01,1,1,1,1,0,1,0,1,11,1,1,1,0,0,1,0,1,01,1,1,1,1,1,0,0,1,11,1,1,1,0,1,0,0,1,01,1,1,1,1,0,0,0,1,01,1,1,1,0,0,0,0,1,01,1,1,0,1,1,1,0,1,01,1,1,0,0,1,1,0,1,11,1,1,0,1,0,1,0,1,11,1,1,0,0,0,1,0,1,11,1,1,0,1,1,0,0,1,11,1,1,0,0,1,0,0,1,01,1,1,0,1,0,0,0,1,11,1,1,0,0,0,0,0,1,00,1,1,1,1,1,1,0,1,00,1,1,1,0,1,1,0,1,00,1,1,1,1,0,1,0,1,00,1,1,1,0,0,1,0,1,00,1,1,1,1,1,0,0,1,00,1,1,1,0,1,0,0,1,10,1,1,1,1,0,0,0,1,00,1,1,1,0,0,0,0,1,00,1,1,0,1,1,1,0,1,00,1,1,0,0,1,1,0,1,00,1,1,0,1,0,1,0,1,00,1,1,0,0,0,1,0,1,10,1,1,0,1,1,0,0,1,00,1,1,0,0,1,0,0,1,00,1,1,0,1,0,0,0,1,10,1,1,0,0,0,0,0,1,11,1,0,1,1,1,1,1,1,01,1,0,1,0,1,1,1,1,01,1,0,1,1,0,1,1,1,01,1,0,1,0,0,1,1,1,01,1,0,1,1,1,0,1,1,01,1,0,1,0,1,0,1,1,01,1,0,1,1,0,0,1,1,01,1,0,1,0,0,0,1,1,01,1,0,0,1,1,1,1,1,11,1,0,0,0,1,1,1,1,01,1,0,0,1,0,1,1,1,01,1,0,0,0,0,1,1,1,01,1,0,0,1,1,0,1,1,01,1,0,0,0,1,0,1,1,01,1,0,0,1,0,0,1,1,11,1,0,0,0,0,0,1,1,00,1,0,1,1,1,1,1,1,00,1,0,1,0,1,1,1,1,00,1,0,1,1,0,1,1,1,00,1,0,1,0,0,1,1,1,10,1,0,1,1,1,0,1,1,00,1,0,1,0,1,0,1,1,00,1,0,1,1,0,0,1,1,00,1,0,1,0,0,0,1,1,10,1,0,0,1,1,1,1,1,00,1,0,0,0,1,1,1,1,00,1,0,0,1,0,1,1,1,00,1,0,0,0,0,1,1,1,00,1,0,0,1,1,0,1,1,00,1,0,0,0,1,0,1,1,10,1,0,0,1,0,0,1,1,00,1,0,0,0,0,0,1,1,01,1,0,1,1,1,1,0,1,01,1,0,1,0,1,1,0,1,01,1,0,1,1,0,1,0,1,01,1,0,1,0,0,1,0,1,01,1,0,1,1,1,0,0,1,01,1,0,1,0,1,0,0,1,01,1,0,1,1,0,0,0,1,01,1,0,1,0,0,0,0,1,01,1,0,0,1,1,1,0,1,11,1,0,0,0,1,1,0,1,01,1,0,0,1,0,1,0,1,11,1,0,0,0,0,1,0,1,01,1,0,0,1,1,0,0,1,01,1,0,0,0,1,0,0,1,01,1,0,0,1,0,0,0,1,01,1,0,0,0,0,0,0,1,10,1,0,1,1,1,1,0,1,00,1,0,1,0,1,1,0,1,00,1,0,1,1,0,1,0,1,10,1,0,1,0,0,1,0,1,00,1,0,1,1,1,0,0,1,00,1,0,1,0,1,0,0,1,10,1,0,1,1,0,0,0,1,00,1,0,1,0,0,0,0,1,00,1,0,0,1,1,1,0,1,00,1,0,0,0,1,1,0,1,00,1,0,0,1,0,1,0,1,00,1,0,0,0,0,1,0,1,00,1,0,0,1,1,0,0,1,00,1,0,0,0,1,0,0,1,00,1,0,0,1,0,0,0,1,00,1,0,0,0,0,0,0,1,01,0,1,1,1,1,1,1,1,01,0,1,1,0,1,1,1,1,01,0,1,1,1,0,1,1,1,01,0,1,1,0,0,1,1,1,11,0,1,1,1,1,0,1,1,01,0,1,1,0,1,0,1,1,01,0,1,1,1,0,0,1,1,11,0,1,1,0,0,0,1,1,11,0,1,0,1,1,1,1,1,11,0,1,0,0,1,1,1,1,01,0,1,0,1,0,1,1,1,11,0,1,0,0,0,1,1,1,11,0,1,0,1,1,0,1,1,01,0,1,0,0,1,0,1,1,01,0,1,0,1,0,0,1,1,11,0,1,0,0,0,0,1,1,00,0,1,1,1,1,1,1,1,00,0,1,1,0,1,1,1,1,00,0,1,1,1,0,1,1,1,00,0,1,1,0,0,1,1,1,00,0,1,1,1,1,0,1,1,00,0,1,1,0,1,0,1,1,00,0,1,1,1,0,0,1,1,00,0,1,1,0,0,0,1,1,00,0,1,0,1,1,1,1,1,00,0,1,0,0,1,1,1,1,00,0,1,0,1,0,1,1,1,00,0,1,0,0,0,1,1,1,10,0,1,0,1,1,0,1,1,10,0,1,0,0,1,0,1,1,00,0,1,0,1,0,0,1,1,00,0,1,0,0,0,0,1,1,01,0,1,1,1,1,1,0,1,11,0,1,1,0,1,1,0,1,01,0,1,1,1,0,1,0,1,11,0,1,1,0,0,1,0,1,11,0,1,1,1,1,0,0,1,01,0,1,1,0,1,0,0,1,01,0,1,1,1,0,0,0,1,11,0,1,1,0,0,0,0,1,01,0,1,0,1,1,1,0,1,11,0,1,0,0,1,1,0,1,11,0,1,0,1,0,1,0,1,01,0,1,0,0,0,1,0,1,01,0,1,0,1,1,0,0,1,11,0,1,0,0,1,0,0,1,01,0,1,0,1,0,0,0,1,01,0,1,0,0,0,0,0,1,00,0,1,1,1,1,1,0,1,00,0,1,1,0,1,1,0,1,10,0,1,1,1,0,1,0,1,00,0,1,1,0,0,1,0,1,00,0,1,1,1,1,0,0,1,00,0,1,1,0,1,0,0,1,00,0,1,1,1,0,0,0,1,10,0,1,1,0,0,0,0,1,00,0,1,0,1,1,1,0,1,00,0,1,0,0,1,1,0,1,00,0,1,0,1,0,1,0,1,00,0,1,0,0,0,1,0,1,10,0,1,0,1,1,0,0,1,00,0,1,0,0,1,0,0,1,00,0,1,0,1,0,0,0,1,10,0,1,0,0,0,0,0,1,11,0,0,1,1,1,1,1,1,11,0,0,1,0,1,1,1,1,01,0,0,1,1,0,1,1,1,11,0,0,1,0,0,1,1,1,01,0,0,1,1,1,0,1,1,01,0,0,1,0,1,0,1,1,01,0,0,1,1,0,0,1,1,01,0,0,1,0,0,0,1,1,01,0,0,0,1,1,1,1,1,01,0,0,0,0,1,1,1,1,01,0,0,0,1,0,1,1,1,11,0,0,0,0,0,1,1,1,01,0,0,0,1,1,0,1,1,01,0,0,0,0,1,0,1,1,01,0,0,0,1,0,0,1,1,01,0,0,0,0,0,0,1,1,10,0,0,1,1,1,1,1,1,00,0,0,1,0,1,1,1,1,10,0,0,1,1,0,1,1,1,00,0,0,1,0,0,1,1,1,00,0,0,1,1,1,0,1,1,00,0,0,1,0,1,0,1,1,10,0,0,1,1,0,0,1,1,00,0,0,1,0,0,0,1,1,00,0,0,0,1,1,1,1,1,00,0,0,0,0,1,1,1,1,00,0,0,0,1,0,1,1,1,10,0,0,0,0,0,1,1,1,00,0,0,0,1,1,0,1,1,00,0,0,0,0,1,0,1,1,00,0,0,0,1,0,0,1,1,00,0,0,0,0,0,0,1,1,01,0,0,1,1,1,1,0,1,01,0,0,1,0,1,1,0,1,01,0,0,1,1,0,1,0,1,11,0,0,1,0,0,1,0,1,01,0,0,1,1,1,0,0,1,11,0,0,1,0,1,0,0,1,01,0,0,1,1,0,0,0,1,01,0,0,1,0,0,0,0,1,01,0,0,0,1,1,1,0,1,11,0,0,0,0,1,1,0,1,01,0,0,0,1,0,1,0,1,01,0,0,0,0,0,1,0,1,01,0,0,0,1,1,0,0,1,01,0,0,0,0,1,0,0,1,01,0,0,0,1,0,0,0,1,11,0,0,0,0,0,0,0,1,10,0,0,1,1,1,1,0,1,00,0,0,1,0,1,1,0,1,00,0,0,1,1,0,1,0,1,00,0,0,1,0,0,1,0,1,00,0,0,1,1,1,0,0,1,00,0,0,1,0,1,0,0,1,00,0,0,1,1,0,0,0,1,00,0,0,1,0,0,0,0,1,00,0,0,0,1,1,1,0,1,10,0,0,0,0,1,1,0,1,00,0,0,0,1,0,1,0,1,10,0,0,0,0,0,1,0,1,10,0,0,0,1,1,0,0,1,00,0,0,0,0,1,0,0,1,00,0,0,0,1,0,0,0,1,00,0,0,0,0,0,0,0,1,01,1,1,1,1,1,1,1,0,01,1,1,1,0,1,1,1,0,01,1,1,1,1,0,1,1,0,01,1,1,1,0,0,1,1,0,01,1,1,1,1,1,0,1,0,01,1,1,1,0,1,0,1,0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And of course if you put the reflector in large distances you will obtain oscillators of different periodic behavior.

Sorry I do not send Golly format.Could somebody explain to me how put the X-Rule in Golly, I copy the .table file that publish M. I. Wright here but I don't know the next step in order that work in Golly?

And of course if you put the reflector in large distances you will obtain oscillators of different periodic behavior.

Sorry I do not send Golly format.Could somebody explain to me how put the X-Rule in Golly, I copy the .table file that publish M. I. Wright here but I don't know the next step in order that work in Golly?

jmgomez wrote:Sorry I do not send Golly format.Could somebody explain to me how put the X-Rule in Golly, I copy the .table file that publish M. I. Wright here but I don't know the next step in order that work in Golly?

You can select dvgrn's rule table and copy, then paste, it into the Golly window (M. I. Wright's tables, as stated, are not the X-Rule). It should then say "created (directory)\x-rule". Then you can just draw in the open window, or paste other patterns in the same way.